Simplify the following expression: $\dfrac{64q^3}{72q^5}$ You can assume $q \neq 0$.
$ \dfrac{64q^3}{72q^5} = \dfrac{64}{72} \cdot \dfrac{q^3}{q^5} $ To simplify $\frac{64}{72}$ , find the greatest common factor (GCD) of $64$ and $72$ $64 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(64, 72) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{64}{72} \cdot \dfrac{q^3}{q^5} = \dfrac{8 \cdot 8}{8 \cdot 9} \cdot \dfrac{q^3}{q^5} $ $\phantom{ \dfrac{64}{72} \cdot \dfrac{3}{5}} = \dfrac{8}{9} \cdot \dfrac{q^3}{q^5} $ $ \dfrac{q^3}{q^5} = \dfrac{q \cdot q \cdot q}{q \cdot q \cdot q \cdot q \cdot q} = \dfrac{1}{q^2} $ $ \dfrac{8}{9} \cdot \dfrac{1}{q^2} = \dfrac{8}{9q^2} $